A306983 Infinitary pseudoperfect numbers: numbers n equal to the sum of a subset of their proper infinitary divisors.

6, 24, 30, 40, 42, 54, 56, 60, 66, 72, 78, 88, 90, 96, 102, 104, 114, 120, 138, 150, 168, 174, 186, 210, 216, 222, 246, 258, 264, 270, 280, 282, 294, 312, 318, 330, 354, 360, 366, 378, 384, 390, 402, 408, 420, 426, 438, 440, 456, 462, 474, 480, 486, 498, 504

Offset: 1

Author

Amiram Eldar, Mar 18 2019

Keywords

• nonn

Comments

Subsequence of A005835.

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A005835, A007357, A049417, A126168, A129656, A293188, A292985, A318100, A306984.

Programs

Mathematica

idivs[x_] := If[x == 1, 1, Sort@Flatten@Outer[Times, Sequence @@ (FactorInteger[x] /. {p_, m_Integer} :> p^Select[Range[0, m], BitOr[m, #] == m &])]]; s = {}; Do[d = Most[idivs[n]]; c = SeriesCoefficient[Series[Product[1 + x^d[[i]], {i, Length[d]}], {x, 0, n}], n]; If[c > 0, AppendTo[s, n]], {n, 2, 1000}]; s